Is it possible that a joule thief will break sensitive components with too much current?

 

Yes. Many thing are possible.

Which Joule Thief circuit? What sensitive component?

 

The basic joule thief circuits with like an inductor and a capacitor and maybe a transistor; I don't know. I just want to know are they trying to force current down components' throats (by increasing voltage until it accepts a certain current) or do they just increase the voltage and let components draw the current they want. I was thinking about modifying a battery powered air-freshener which uses a mechanism to depress the button on a spray can but I sometimes think about using them in other situations as well.

 

Your suspicion is confirmed.

In what I think of as the classic Joule Thief (transistor, center tapped inductor, resistor, LED) the LED is driven by current pulses. If the current is too high parts can be damaged.

In the case in which a rectifier and smoothing capacitor is used, the voltage across the capacitor is a function of the LED's voltage at a constant current.